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If A and B are two independent events in a given sample space and the probability that both A and B occur is 0.16 while the probability that neither occurs is 0.36. The probabilities P(A) and P(B) are respectively
- a)0.6, 0.6
- b)0.8, 0.2
- c)0.4, 0.4
- d)0.9, 0.4
Correct answer is option 'C'. Can you explain this answer?
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If A and B are two independent events in a given sample space and the ...
Given Information:
- Probability of both A and B occurring (P(A ∩ B)) = 0.16
- Probability of neither A nor B occurring (P(A' ∩ B')) = 0.36
Solution:
Understanding Independent Events:
- Two events A and B are independent if the occurrence of one event does not affect the occurrence of the other event.
- Mathematically, for independent events A and B, P(A ∩ B) = P(A) * P(B)
Calculation:
- Let P(A) = x and P(B) = y
- Given P(A ∩ B) = 0.16
- P(A ∩ B) = P(A) * P(B) = x * y = 0.16
Substitute values:
- From the given data, we have P(A ∩ B) = 0.16
- Substitute x * y = 0.16
Probability of Neither A nor B:
- P(A' ∩ B') = P(A') * P(B') = (1 - P(A)) * (1 - P(B))
- Given P(A' ∩ B') = 0.36
Calculate P(A) and P(B):
- We have (1 - x) * (1 - y) = 0.36
- Solve the above equation to find the values of x and y
Therefore, the probabilities P(A) and P(B) are 0.4 each, which corresponds to option 'C'.
- Probability of both A and B occurring (P(A ∩ B)) = 0.16
- Probability of neither A nor B occurring (P(A' ∩ B')) = 0.36
Solution:
Understanding Independent Events:
- Two events A and B are independent if the occurrence of one event does not affect the occurrence of the other event.
- Mathematically, for independent events A and B, P(A ∩ B) = P(A) * P(B)
Calculation:
- Let P(A) = x and P(B) = y
- Given P(A ∩ B) = 0.16
- P(A ∩ B) = P(A) * P(B) = x * y = 0.16
Substitute values:
- From the given data, we have P(A ∩ B) = 0.16
- Substitute x * y = 0.16
Probability of Neither A nor B:
- P(A' ∩ B') = P(A') * P(B') = (1 - P(A)) * (1 - P(B))
- Given P(A' ∩ B') = 0.36
Calculate P(A) and P(B):
- We have (1 - x) * (1 - y) = 0.36
- Solve the above equation to find the values of x and y
Therefore, the probabilities P(A) and P(B) are 0.4 each, which corresponds to option 'C'.
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If A and B are two independent events in a given sample space and the probability that both A and B occur is 0.16 while the probability that neither occurs is 0.36. The probabilities P(A) and P(B) are respectivelya)0.6, 0.6b)0.8, 0.2c)0.4, 0.4d)0.9, 0.4Correct answer is option 'C'. Can you explain this answer?
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If A and B are two independent events in a given sample space and the probability that both A and B occur is 0.16 while the probability that neither occurs is 0.36. The probabilities P(A) and P(B) are respectivelya)0.6, 0.6b)0.8, 0.2c)0.4, 0.4d)0.9, 0.4Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If A and B are two independent events in a given sample space and the probability that both A and B occur is 0.16 while the probability that neither occurs is 0.36. The probabilities P(A) and P(B) are respectivelya)0.6, 0.6b)0.8, 0.2c)0.4, 0.4d)0.9, 0.4Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A and B are two independent events in a given sample space and the probability that both A and B occur is 0.16 while the probability that neither occurs is 0.36. The probabilities P(A) and P(B) are respectivelya)0.6, 0.6b)0.8, 0.2c)0.4, 0.4d)0.9, 0.4Correct answer is option 'C'. Can you explain this answer?.
If A and B are two independent events in a given sample space and the probability that both A and B occur is 0.16 while the probability that neither occurs is 0.36. The probabilities P(A) and P(B) are respectivelya)0.6, 0.6b)0.8, 0.2c)0.4, 0.4d)0.9, 0.4Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If A and B are two independent events in a given sample space and the probability that both A and B occur is 0.16 while the probability that neither occurs is 0.36. The probabilities P(A) and P(B) are respectivelya)0.6, 0.6b)0.8, 0.2c)0.4, 0.4d)0.9, 0.4Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A and B are two independent events in a given sample space and the probability that both A and B occur is 0.16 while the probability that neither occurs is 0.36. The probabilities P(A) and P(B) are respectivelya)0.6, 0.6b)0.8, 0.2c)0.4, 0.4d)0.9, 0.4Correct answer is option 'C'. Can you explain this answer?.
Solutions for If A and B are two independent events in a given sample space and the probability that both A and B occur is 0.16 while the probability that neither occurs is 0.36. The probabilities P(A) and P(B) are respectivelya)0.6, 0.6b)0.8, 0.2c)0.4, 0.4d)0.9, 0.4Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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